yield strength

So I know you said to use an offset of 0.02% or 0.05% and the elastic modulus as the slope in order to calculate the yield strength but how do you find this value because you only have one value of strain and one value of stress that are known. You would set the slope=(y2 -y1)/(x2-x1) where y is stress and x is strain, but you only know the initial strain and initial stress right? So how do you solve for the yield strength if you have two unknowns in this equation?

The offset you use will depend on how you quote your standard, but the offset is the strain that you are going to use. For instance, if your quoted standard is yield with 0.2% offset, you are going to draw a strain line, with the slope of the elastic modulus starting at 0.2% until it intersects the curve, and that will give you the yield stress at 0.2% offset.